- Arithm etic Sequences Use the arithm etic seq u en ce 10,15, 20, 25, ...
a. Find the co m m o n difference of th e sequence.
b. Let x = th e term n um ber, a n d let y = the corresponding term of the sequence.
G raph th e ordered pairs (x, y) for th e first eight term s of th e sequence. Draw a
line th rough th e points.
c. R easo ning How is th e slope of a line from p a rt (b) related to th e com m on
difference of the sequence?
Challenge Do the points in each set lie on the same line? Explain your answer.- A (l, 3), B(4, 2), C(—2, 4) 51. G(3, 5), 7 f ( - 1, 3), 7(7, 7) 52. D ( - 2 , 3), £(0, - 1 ) , F{2,1)
- P(4, 2), Q ( - 3, 2), 7?(2, 5) 54. G(l, - 2 ) , 7 / ( - l , - 5 ) , 7(5, 4) 55. S (-3 , 4), 7t0, 2 ),X (- 3 , 0)
Find the slope of the line that passes through each pair of points.- (a, - b ) , ( - a , -b) 57. (—m, ri), (3m, -ri) 58. (2fl, b), (c, 2d)
Apply What You've Learned
The table at the right shows the height of w ater in a glass w h en different
n u m b ers of m arbles are d ro p p e d into it.a. Find th e rate of change in the w ater height w ith respect to the
n u m b e r of m arbles from one row in the table to th e next.
W hat do you notice?
b. For each m arble you add to th e glass, how m u ch does the
w ater level rise?
c. W hat can you conclude about the type of function th a t m odels
the relationship betw een the n u m b e r of m arbles an d th e w ater
height? Explain.MATHEMATICAL
PRACTICES
MP 1(^3) 6.9
5 7.5
9 8.7
(^14) 10.2
(^17) 11.1
(^23) 12.9
300 Ch ap t er 5 Li n ear Fu n ct i o n s